Macbi wrote:In fact I already figured out a bit about the positioning of the cells and the rules.

If you want a 2-cell high-period oscillator the two cells have to be one cell apart orthogonally. Then you have to have B2i, S0, B2a, S1e. You can't have B0, B1c, B1e, B2c, B3i.

So to search for 2 cell oscillators you can set LLS up with two cells one cell apart in some size of bounding box and enforce the rules I mentioned.

Then all LLS is doing is searching through all remaining rules to find an oscillator of the given period.

This is pretty much the method (and rule restrictions I followed), although I also enforced D4+ symmetry and forgot about the -c option (instead I enforced the center cell on in relevant generations). There is however an alternate set of rule restrictions: here are a few high period oscillators without S0 and with B2c in their rule specification:

p30, 2 cells

`x = 3, y = 1, rule = B2aci4aintw/S1e2ai4ei5y`

obo!

p32, 2 cells

`x = 3, y = 1, rule = B2aci4aintw/S1e2ai4ei5y`

obo!

p34, 2 cells

`x = 3, y = 1, rule = B2-kn3e4t5iqy6i/S12i3eqy4cerw5iy6c7e8`

obo!

p36, 2 cells

`x = 3, y = 1, rule = B2acei4cr5e7e/S1e2cik3enr4aet`

obo!

p62, 2 cells

`x = 3, y = 1, rule = B2-ek3n4ctw/S12i3ace5i`

obo!

Here are a few more reductions down to 2 cells for even periods:

p60, 2 cells

`x = 3, y = 1, rule = B2aei3q4ceinr5j6ci7e/S01e2ek3-acnq4eiknqr5aeiy7e`

obo!

p64, 2 cells

`x = 3, y = 1, rule = B2aik3any4eikt5eiy6e8/S01e2-an3knry4-nqtw5iky7e`

obo!

p66, 2 cells

`x = 3, y = 1, rule = B2ai3k4cinqty5ijy7e8/S01e2eik3jry4acint5cijny6ac7e`

obo!

p68, 2 cells

`x = 3, y = 1, rule = B2ai3aen4ajnrt5eikny6ce7e8/S01e2ei3acery4aceirwy5ceky6c`

obo!

Edit: (I couldn't resist)

p70, 2 cells

`x = 3, y = 1, rule = B2ain3acr4eijnwy5-jkny6-cn7e/S01e2-ai3-in4jknty5-qr6-in7e8`

obo!

p72, 2 cells

`x = 3, y = 1, rule = B2aei3cjqy4-aet5-q6ace7e8/S01e2ei3aijkr4ackw5acer6ack`

obo!

p74, 2 cells

`x = 3, y = 1, rule = B2-ck3aeky4eir5jy8/S01e2eik3en4acnqt5ciny6cek7e`

obo!

p76, 2 cells

`x = 3, y = 1, rule = B2aei3enq4eijkq5ceny6ci7e/S01e2eik3cinr4enrt5-jkr6ei`

obo!

p78, 2 cells

`x = 3, y = 1, rule = B2aei3aenq4aiktw5ae6cei8/S01e2ein3-ain4aijkn5ry6ci`

obo!

Most of those searches only took a few minutes. For some reason p80 is taking much longer.

[/edit]

Edit 2:p80, 2 cells (30 mins in lls)

`x = 3, y = 1, rule = B2aei3acen4aciy5einy6i/S01e2in3aejy4acejn5ij6ac7e`

obo!

p82, 2 cells (20 mins in lls)

`x = 3, y = 1, rule = B2aei3ekqry4jnr5cej6ci7e8/S01e2eik3ejnr4cirt5jy6ce7e8`

obo!

If anyone is curious, this is the method I've been using to find these (example for p78, 2 minutes search time):

`$ python make_lls_grid.py -p 39 -m 90 -f 3 3 5 7 > osc.txt`

$ python lls osc.txt -r pB2ai3-i45678/S012345678 --force_at_most 2 -s "D4+" -m -c 0 2 -c 0 6

[/edit]

Edit 3:p84, 2 cells

`x = 3, y = 1, rule = B2ai3acejq4eky5eijy6ae7e8/S01e2cei3-ciny4-ejqrz5-cejr7e8`

obo!

p86, 2 cells

`x = 3, y = 1, rule = B2aei3cekqy4-acrt5-aeij6-n7e8/S01e2ekn3einr4nqrtwy5-eqr6ack7e`

obo!

[/edit]

Macbi wrote:77topaz wrote:I wonder, what is that maximum period? Is that even calculable with current technology?

More possible to answer would be "What's the minimum period not achievable?".

Even that might be problematic, because there's no easy way to define a limit on what the bounding box of the oscillator is or what its maximum population is. There's probably a way, but I can't see how you rule out an extremely high period oscillator which grows and grows and then suddenly collapses back down to 2 cells. I suspect though that any upper bound would be astronomically larger than the true value.